Algebra Examples

$y = - x (x + 3) (x - 3)$

Step 1

Simplify the polynomial, then reorder it left to right starting with the highest degree term.

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Step 1.1

Apply the distributive property.

$y = (- x \cdot x - x \cdot 3) (x - 3)$

Step 1.2

Multiply $x$ by $x$ by adding the exponents.

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Step 1.2.1

Move $x$ .

$y = (- (x \cdot x) - x \cdot 3) (x - 3)$

Step 1.2.2

Multiply $x$ by $x$ .

$y = (- x^{2} - x \cdot 3) (x - 3)$

Step 1.3

Multiply $3$ by $- 1$ .

$y = (- x^{2} - 3 x) (x - 3)$

Step 1.4

Expand $(- x^{2} - 3 x) (x - 3)$ using the FOIL Method.

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Step 1.4.1

Apply the distributive property.

$y = - x^{2} (x - 3) - 3 x (x - 3)$

Step 1.4.2

Apply the distributive property.

$y = - x^{2} x - x^{2} \cdot - 3 - 3 x (x - 3)$

Step 1.4.3

Apply the distributive property.

$y = - x^{2} x - x^{2} \cdot - 3 - 3 x \cdot x - 3 x \cdot - 3$

Step 1.5

Simplify and combine like terms.

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Step 1.5.1

Simplify each term.

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Step 1.5.1.1

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 1.5.1.1.1

Move $x$ .

$y = - (x \cdot x^{2}) - x^{2} \cdot - 3 - 3 x \cdot x - 3 x \cdot - 3$

Step 1.5.1.1.2

Multiply $x$ by $x^{2}$ .

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Step 1.5.1.1.2.1

Raise $x$ to the power of $1$ .

$y = - (x \cdot x^{2}) - x^{2} \cdot - 3 - 3 x \cdot x - 3 x \cdot - 3$

Step 1.5.1.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = - x^{1 + 2} - x^{2} \cdot - 3 - 3 x \cdot x - 3 x \cdot - 3$

Step 1.5.1.1.3

Add $1$ and $2$ .

$y = - x^{3} - x^{2} \cdot - 3 - 3 x \cdot x - 3 x \cdot - 3$

Step 1.5.1.2

Multiply $- 3$ by $- 1$ .

$y = - x^{3} + 3 x^{2} - 3 x \cdot x - 3 x \cdot - 3$

Step 1.5.1.3

Multiply $x$ by $x$ by adding the exponents.

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Step 1.5.1.3.1

Move $x$ .

$y = - x^{3} + 3 x^{2} - 3 (x \cdot x) - 3 x \cdot - 3$

Step 1.5.1.3.2

Multiply $x$ by $x$ .

$y = - x^{3} + 3 x^{2} - 3 x^{2} - 3 x \cdot - 3$

Step 1.5.1.4

Multiply $- 3$ by $- 3$ .

$y = - x^{3} + 3 x^{2} - 3 x^{2} + 9 x$

Step 1.5.2

Subtract $3 x^{2}$ from $3 x^{2}$ .

$y = - x^{3} + 0 + 9 x$

Step 1.5.3

Add $- x^{3}$ and $0$ .

$y = - x^{3} + 9 x$

Step 2

The degree of a polynomial is the highest degree of its terms.

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Step 2.1

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

$- x^{3} \to 3$

$9 x \to 1$

Step 2.2

The largest exponent is the degree of the polynomial.

$3$

Step 3

The leading term in a polynomial is the term with the highest degree.

$- x^{3}$

Step 4

The leading coefficient of a polynomial is the coefficient of the leading term.

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Step 4.1

The leading term in a polynomial is the term with the highest degree.

$- x^{3}$

Step 4.2

The leading coefficient in a polynomial is the coefficient of the leading term.

$- 1$

Step 5

List the results.

Polynomial Degree: $3$

Leading Term: $- x^{3}$

Leading Coefficient: $- 1$